Contact processes with long-range interactions

TL;DR

This paper introduces and analyzes a class of non-local contact processes with algebraically decaying creation rates, revealing continuous phase transitions with varying critical exponents, relevant to non-equilibrium wetting phenomena.

Contribution

It presents a new non-local contact process model with algebraic decay and studies its critical behavior, differing from previous Levy flight models.

Findings

Transition into the absorbing state is continuous.

Critical exponents vary continuously.

Model is relevant to non-equilibrium wetting studies.

Abstract

A class of non-local contact processes is introduced and studied using mean-field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest particle. It is found that the transition into the absorbing state is continuous and is characterized by continuously varying critical exponents. This model differs from the previously studied non-local directed percolation model, where particles are created by unrestricted Levy flights. It is motivated by recent studies of non-equilibrium wetting indicating that this type of non-local processes play a role in the unbinding transition. Other non-local processes which have been suggested to exist within the context of wetting are considered as well.